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Liula [17]
3 years ago
13

WhichGiven that f(x) = x² + 5x, evaluate f(-2). of the following is equal to ?

Mathematics
1 answer:
Andrew [12]3 years ago
4 0
F(x)= x²+5x
f(x)= -2²+5(-2)
f(x)= 4-10
f(x)= -6
I hope I helped you :)
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Find the intervals on which​ f(x) is​ increasing, the intervals on which​ f(x) is​ decreasing, and the local extrema. f (x )equa
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Answer:

f(x) is increasing in the intervals (-∞,-4) and (9,∞)

f(x) is decreasing in the ingercal (-4,9)

The local extrema is:

local max at (-4,496)

and local min at (9,-1701)

Step-by-step explanation:

In order to solve this problem we must start by finding the derivative of the provided function, which we can find by using the power rule.

if f(x)=ax^{n} then f'(x)=anx^{n-1}

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f(x)=2x^{3}-15x^{2}-216x

f'(x)=6x^{2}-30x-216

in order to find the critical points we mus set the derivative equal to zero, since the local max an min will happen when the slope of the tangent line to the given point is zero, so we get:

6x^{2}-30x-216=0

we can solve this by factoring, so let's factor that equation:

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we can now set each of the factors equal to zero so we get:

x+4=0 and x-9=0

when solving each for x we get that:

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We can see that at x=9, the function it's decreasing on the left of this point while it's increasing to the right, which means that there will be a local minimum at x=-9, so the local min is the point (9,-1701)

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3 years ago
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