Question

For the function F(x)=(1/3)x^3 +x^2 -3x +6, find the coordinates of the points with zero gradients and sketch the graph of F(x), showing the turning points and y-intercept

Answer 1

so
\[\large F(x)=\frac 13 x^3 +x^2 -3x +6\]
points with zero gradients:
first find derivative of F(x)
make F'(x) = 0
sub those x coordinates found back into F(x) to get y coordinates
=turning points of function

Answer 2

y intercept can be read straight off original function
\[F(x)=(1/3)x^3 +x^2 -3x +6\]
\[F(x)= a x^3 + bx^2 -cx +d\]
y intercept is "d"

Answer 3

thankyou!