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alexandr1967 [171]
3 years ago
10

Help with functions?

Mathematics
1 answer:
ivolga24 [154]3 years ago
5 0

Answer:

The function g(x) = - x² + 14x + 39 is at a minimum when x = 7 is not true i.e. false.

Step-by-step explanation:

The function is given to be g(x) = - x² + 14x + 39 .......... (1)

Now, the condition for maxima or minima is g'(x) = \frac{dg(x)}{dx} = 0.

Now, differentiating equation (1) we get, g'(x) = - 2x + 14 ........ (2)

Hence, for maxima or minima g'(x) = 0 = - 2x + 14

⇒ x = 7

Now, from equation (2) and differentiating both sides with respect to x again g"(x) = \frac{d^{2}g(x) }{dx^{2} } = -2 < 0

Therefore,the function g(x) has maxima at x = 7

Therefore, the function g(x) = - x² + 14x + 39 is at a minimum when x = 7 is not true i.e. false.

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