a. find the derivative of f at x. that is, fi...
a. find the derivative of f at x. that is, find f(x) b. find the slope of the tangent line to the graph of f at each of the two values of x given to the right of the function. f(x)=3.9x² + 5.7x; x=-1, x = 4 a. f(x)=7.8x + 5.7 (simplify your answer. use integers or decimals for any numbers in the expression.) b. at x=-1, the slope of the tangent line to the graph of f is -2.1 (type an integer or a decimal.) at x = 4, the slope of the tangent line to the graph of f is (type an integer or a decimal.)
Answer
# Explanation:
## Step1: Recall derivative formula
For $f(x)=ax^2 + bx + c$, $f'(x)=2ax + b$. Given $f(x)=3.9x^2+5.7x$, so $a = 3.9$ and $b = 5.7$. Then $f'(x)=2\times3.9x+5.7=7.8x + 5.7$.
## Step2: Find slope at $x = 4$
Substitute $x = 4$ into $f'(x)$. We get $f'(4)=7.8\times4+5.7$.
$f'(4)=31.2 + 5.7=36.9$.
# Answer:
$36.9$