“Finding the Equation of a Tangent Line with Derivatives”
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at the point 
.
.
.
?
and ellipse 
intersect?
at the point 
.
have a gradient 
?
at the point 
in the three forms. At what points does the tangent intersect the coordinate axis?
at point 
at the abscissa x = - 1 parallel to the line 
?
which is parallel to the x-axis. Also write the equation of the normal that is parallel to the bisector of the even quadrants.
that go through the point T (0, 24).
has tangents with the gradient 3.
intersects the abscissa axis.
on the function 
. Calculate the point of intersection of the normal and the function, and obtain the equation of the normal.
and 
.
have an inclination angle 
?
intersects the ordinate axis.
with an angle of inclination 
.
and 
are given.
and 
so that the graph of the polynomial 
passes through points 
and 
. Then calculate the stationary points of this polynomial.
axis only at the point 
at the point 
.
and 
.
at the point 
.
at the point 
.
at the point of intersection with the ordinate axis.
for which 
is a tangent to the graph of the function 
.
at the point of intersection with the abscissa axis.
at the point 
.
at the point 
.
at the intersection of the curve with the y-axis.
at the point 
.
at the point 
.
at point 
.
is given. Obtain the coordinates of the vertex of the triangle enclosed by the coordinate axes and the tangent to the function f at the point 
.
is increasing and decreasing.
is increasing and decreasing.
is increasing and decreasing.
is increasing and decreasing.
is increasing and decreasing.
is increasing and decreasing:
and obtain its turning points.
at the point 
in three forms.
parallel to the line 
?
are parallel to the line 
.
and obtain the turning points.
and obtain the stationary points.
, which is parallel to the bisectors of the even quadrants.
which has an inclination angle 
? Also write down the coordinates of the tangent.
does the tangent have an inclination angle 
? Hence, calculate the equation of normal to curve at this point.
at the point 
.
intersects the abscissa axis?
intersect the abscissa axis?
at the point where the abscissa is 2?
intersect the ordinate axis?
parallel to the abscissa axis.
and 
.
and 
.
, obtain the zeros, the intersection with the ordinate axis and local maxima.
.
.
.
.
, 
.
at point 
.
which are parallel to the line 
.
cm, find the value of the sides a and b which gives the maximum area.
, obtain the zeros, intersection with ordinate axis, the stationary points and hence draw the graph.
, obtain the zeros, intersection with the ordinate axis, the stationary points and sketch the graph of the given function.
. Obtain the zeros, domain, intersection with the ordinate axis, asymptote and the stationary points.
obtain the zeros, domain, intersection with ordinate axis, asymptotes and the turning points.
obtain the zeros, points of discontinuity, intersection with ordinate axis, asymptotes and the turning points.
at the point of intersection with the ordinate axis?
intersects the abscissa axis?
, obtain the zeros, the intersection with the ordinate axis and the turning point.
as shown below.
. The result should be accurate.
.
axis.
and the function intersect at the point with abscissa 
.
and 
, 
.
for every 
is equal to 
.
.
and 
are drawn on the circle so that the angles 
and 
are right angles (as shown in the diagram below for one of the possible drawn situations). The size of the angle 
depends on the selection of the positions of the points 
and 
and 
drawn in this way, the area of the shaded area as a function of the size of the angle 
is equal to 
, if the angle 
is expressed in radians.
, the width of the tunnel is 
, and its length is 
. The curved ceiling and walls of the tunnel will be painted over. For this purpose, 400 l of paint was bought. Will there be enough paint if they use exactly 5 l of paint for 
? Justify your answer.
and plot its graph in the given coordinate system.
.
from the coordinate origin. Round the result to two significant figures.
at two points. Calculate the exact coordinates of the points of intersection 
and 
.
, 
and 
are given in a plane. By mirroring the point B over the line 
, the point D is gotten.
around the side AC to get the geometric shape G. Prove that the volume of the solid G is 
, where 
and 
.
with unknown x and a constant m.
and 
.
have a turning point at 
?
and 
, and the length of the side 
.
is equal to 
. Calculate the size of the angle 
. Round the result to the nearest minute.
. Calculate the length of 
.
is equal to 
. There is a point T on the side AD and a point V on the side AB such that 
. Calculate at what length 
the area of the triangle VBT will be maximum.
.
.
is maximum.
for all 
and 
.
.
of the point A from the line 
and the distance 
of the point A from the line 
.
.
be such points on the unit circle that the quadrilateral ABCD is a trapezium with bases AB and CD. The diagonals of the trapezium intersect at the point P.
be the size of the angle AOB.
and 
and prove that the trapezium ABCD is orthodiagonal.
in term of 
at a point 
. Obtain the equation of this line.
and the circle 
? Justify your answer.
.
lies on the line 
