SOLUTION: Let f (x) = 2x^2 + 8x-1
(a) Find the derivative f ’ of f.
(b) Find an equation of the tangent line to the point of (1,3).
(c) Determine whether the critical point gives
Algebra ->
Functions
-> SOLUTION: Let f (x) = 2x^2 + 8x-1
(a) Find the derivative f ’ of f.
(b) Find an equation of the tangent line to the point of (1,3).
(c) Determine whether the critical point gives
Log On
Question 476981: Let f (x) = 2x^2 + 8x-1
(a) Find the derivative f ’ of f.
(b) Find an equation of the tangent line to the point of (1,3).
(c) Determine whether the critical point gives maximum or minimum f value and find the value.
Do appreciate your help. Thanking you in advance Answer by robertb(5830) (Show Source):
You can put this solution on YOUR website! (a) f'(x) = 4x+8
(b) (1,3) is NOT a point on the parabola.
(c) You don't need calculus to know if there is a max or a min, it's obvious from the coefficient of that the function has an (absolute) min.
BUT if you insist, then f'(x) = 4x+8 = 0 ==> x = -2.
The 2nd derivative is f"(x) = 4 > 0, so by the 2nd derivative test there is (absolute) min at x = -2. (x = -2 could have been gotten using the good ol' formula .)
