Question

Find the slope of the tangent line to the graph of each function at x= -1

Answer 1

Given:

`f(x)=3x^3+4x^2-10x+7`

Required:

To find the slope of the tangent line to the graph of each function at x= -1​.

Step-by-step explanation:

Consider the given function

`f(x)=3x^3+4x^2-10x+7`
`f^(\prime)(x)=9x^2+8x-10`

At x=-1,

`\begin{gathered} f^(\prime)(-1)=9(-1)^2+8(-1)-10 \\ \\ =9-8-10 \\ \\ =-9 \end{gathered}`

Final Answer:

The slope is -9.