Home > Calculus > Slope of a Curve at a Point

How do you find the slope of the tangent to the curve #y = 3 + 4x^2 - 2x^3# where x = a?

Answer 1

Ezekiel Alexander

The derivative of a function is the slope of the tangent to that function.

Given #y=3+4x^2−2x^3#

#(dy)/(dx) = 8x -6x^2#

So the slope of the tangent to the curve at #x=a# is #8a -6a^2#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Paisley Johnson

To find the slope of the tangent to the curve y = 3 + 4x^2 - 2x^3 at x = a, you need to find the derivative of the function y with respect to x, then evaluate it at x = a. The derivative of the function y = 3 + 4x^2 - 2x^3 is given by:

dy/dx = d/dx(3 + 4x^2 - 2x^3)

dy/dx = 0 + 8x - 6x^2

Now, to find the slope of the tangent at x = a, substitute a for x in the derivative:

Slope = dy/dx at x = a = 8a - 6a^2

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.