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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.
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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.
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Mathematics
3 years
2021-08-31T13:13:55+00:00
2021-08-31T13:13:55+00:00 1 Answers
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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):