Question

Consider the function f(x)=x^2+5x+2 and the point A(4,2).

f′(x) =? Find a formula for the slope of a line passing through point A, and an arbitrary point on the function. Your answer should be a formula in terms of x.
Slope=? Using your answers from the two previous questions, find the slope(s) of the line(s) through point A that is (are) tangent to f(x). If there is more than one line you can separate your answers with a comma (ex. 5, 2). slope(s) =?

Answer 1

To find the slope, we need to find the derivative of f(x). It is as follows:

f(x) = x^2+5x+2
f'(x) = 2x + 5, f'(x) = 13

Therefore, the slope is 13. Hope this answers the question. Have a nice day.