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mafiozo [28]
4 years ago
6

Suppose g(x) = x^2f(x) and it is known that f(3) = 5 and f '(3) = −2. Evaluate g'(3).

Mathematics
1 answer:
vlabodo [156]4 years ago
7 0

g'(x)=(x^2)'(f(x))+(f'(x))(x^2)

g'(x)=(2x)(f(x))+(f'(x))(x^2)

for g'(3)

g'(3)=(2(3))(f(3))+(f'(3))(3^2)

g'(3)=(6)(5)+(-2)(9)

g'(3)=30-18

g'(3)=12


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We see that in these 3 terms, 6 is a common factor. So, let's factor out a 6:

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We can set this equal to 0 and factor by using the quadratic formula which is:

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So, let's do just that:

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Note that the 6 goes away if you divide both sides by 6. In this case, a = 1, b = -1, and c = -2. Let's plug that into the quadratic equation:

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