What is the extreme f(x)=-3x^2+2x-4,1<= x<= 4 ?

The extreme f(x)=-3x^2+2x-4,1<= x<= 4 is Maximum(1,-5),Minimum(4,-44)

Popular >

extreme f(x)=-3x^2+2x-4,1<= x<= 4

extreme points

f (x) = - 3 x^{2} + 2 x - 4, 1 \leq x \leq 4

Maximum (1, - 5), Minimum (4, - 44)

Solution steps

Find the critical points:

x = 1, x = 4

Domain of

- 3 x^{2} + 2 x - 4, 1 \leq x \leq 4 : 1 \leq x \leq 4

Find intervals:

Decreasing

: 1 < x < 4

Plug the extreme point

x = 1

into

- 3 x^{2} + 2 x - 4 \Rightarrow y = - 5

Maximum (1, - 5)

Plug the extreme point

x = 4

into

- 3 x^{2} + 2 x - 4 \Rightarrow y = - 44

Minimum (4, - 44)

Maximum (1, - 5), Minimum (4, - 44)

R (M) = M^{2} (\frac{1}{2} - \frac{M}{3})

f (x) = 8 x^{4} - 5 x^{3} + x^{2} - 2 x + 3

f (x, y) = 400 - 81 x^{2} - 81 y^{2}

f (x) = \frac{1}{2} (x - 2)^{- \frac{1}{2}}

x^{4} + 2 x^{2}

What is the extreme f(x)=-3x^2+2x-4,1<= x<= 4 ?
The extreme f(x)=-3x^2+2x-4,1<= x<= 4 is Maximum(1,-5),Minimum(4,-44)