Can anyone confirm my answers? Using 1st principles to find slope at given x value.

Question

** using the tangent slope method **

A. f(x)=2x^2-6x at x=3

My answer: the slope at x=3 is 6

B. y=3x^3+1 at x=-4

My answer: the slope at x=-4 is 47

Am I on the right track? Or if either answer is incorrect what did I do wrong? How can I improve? Thanks.

Answer 1

Take the derivative of the first function f(x) = 2x² - 6x

The derivative, f '(x) = 4x - 6

At X = 3, the slope is 4(3) - 6 = 12 - 6 = 6!

The derivative of the second function f(x) = 3x³+ 1 is:

f ' (x) = 9x²

At X = -4, the slope then is 9 (-4)² = 9 x 16 = 144

Answer 2

Your first answer is correct.

The derivative in the second problem is 9x².