Share

## What is the equation of the line tangent to the function f(x) = 4x^2 + 5x at the point (-2, 6). Will give brainliest! Thank you.

Question

What is the equation of the line tangent to the function f(x) = 4x^2 + 5x at the point (-2, 6).

Will give brainliest! Thank you.

in progress
0

Mathematics
3 years
2021-08-31T13:13:55+00:00
2021-08-31T13:13:55+00:00 1 Answers
3 views
0
## Answers ( )

Answer:Step-by-step explanation:We want to find the equation of the tangent line to the function:

At the point (-2, 6).

First, we will need the slope of the tangent line. So, differentiate* the function:

Find the slope when

x= -2:Now, we can use the point-slope form:

Our point is (-2, 6) and our slope is -11. Substitute:

Simplify:

Distribute:

And add six to both sides. Therefore, our equation is:

If you have not yet learned differentiation, here’s the method using the difference quotient! The difference quotient is given by:

Here,

x= -2. Substitute:Substitute (we are given the point (-2, 6). So, f(-2) = 6).

Expand and simplify:

Distribute:

Simplify:

Evaluate the limit (using direct substitution):