Question

Compute f'(a).
f(x) = x^2 + 11x, when a = 6

Answer 1

f ' (a)

Answer 2

find f'(x) = 2x + 11 then substitute x = 6 into the derivative to find f'(a)

Answer 3

12+11 = 23

Answer 4

did you all use the power rule? and what about this...
Find f(3) and f'(3), assuming that the tangent line to y = f(x) at a = 3 has equation
y = 6x + 8

Answer 5

how would you find the tangent line equation if you knew f '(X) or just f(x)

Answer 6

f'(x) at a point x = 6 will give the gradient of that tangent at x = 6..... sub x = 6 into the original equation to find the y value... then you have the gradient and point... which can be used the the point slope formula

y - f(a) = f'(a)(x - a) to get the equation of the tangent

Answer 7

so what is a?

Answer 8

in your example where x = 3 then

y - f(3) = f'(3)(x-3)

Answer 9

so 26 - 26 = 6 - 3?