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Johny 5
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Homework Statement
Let f be a function differentiable function with f(2) = 3 and f'(2) = -5, and let g be the function defined by g(x) = xf(x). Which of the following is an equation of the line tangent to the graph of g at point where x=2?
a. y=3x
b y-3 = -5(x-2)
c y-6 = -5(x-2)
d y-3 = -7(x-2)
e y-6 = -10(x-2)
Homework Equations
The Attempt at a Solution
given:
x=2
y=3
so
3=-5(2)+b
b=13
so
g(x) = x(-5x+13)
g(x) = -5x^2 + 13x
g'(x) = -10x +13
g'(2) = -7
point slope form:
d. y-3 = -7(x-2)
is that correct?