What are the extrema of f(x)=-3x^2+30x-74 on [-oo,oo]?

1 Answer
Oct 11, 2017

Let's see.

Explanation:

Let the function given be y such that rarr for any value of x in the given range.

y=f(x)=-3x^2+30x-74

:.dy/dx=-6x+30

:.(d^2y)/dx^2=-6

Now, since the second order derivative of the function is negative, the value of f(x) will be maximum.

Hence, point of maxima or extrema can only be obtained.

Now, whether for maxima or minima,

dy/dx=0

:.-6x+30=0

:.6x=30

:.x=5

Therefore, the point of maxima is 5. (Answer).

So, the maximum value or the extreme value of f(x) is f(5).

:.f(5)=-3.(5)^2+30.5-74

:.f(5)=-75+150-74

:.f(5)=150-149

:.f(5)=1.

Hope it Helps:)