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.

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):

0 is its x and y coordinate