Question

Please solve (a)Suppose that f(x) = 7x^2 + 7.(A) Find the slope of the line tangent to f(x) at x = -1(B) Find the instantaneous rate of change of f(x) at x= -1.(C) Find the equation of the line tangent to f(x) at x=- 1.Y=

Answer 1

Given:

`f(x)=7x^2\text{ + 7}`

To find the slope of the tangent line of the function at the given value, evaluate the first derivative for the given.

The first derivative is:

`\begin{gathered} f^(\prime)(x)=anx^(n-1) \\ f^(\prime)(x)\text{ = 14x } \end{gathered}`

At x =-1:

`\begin{gathered} f^(\prime)(x=-1)\text{ = 14(-1)} \\ =\text{ -14} \end{gathered}`

Hence, the slope is -14