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Application of Derivatives

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Multiple Choice Questions

201.

The interval in which y = x²e^–x is increasing is

(– ∞, ∞)
(– 2, 0)
(2, ∞)
(2, ∞)

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Short Answer Type

202.

Find the maximum and the minimum values, if there be any, of f given by f(x) = 9x²– 6x + 1, x ∊ R.

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203. Find the maximum and the minimum values of f, if there be any, given by
f(x) = – x², x ∊ R

The given function is non-positive for all x ∊ R
Also, f (x) = 0 if x = 0. Therefore, the maximum value of f is 0 and the point of maximum value of f is x.
Further, note that f has no minimum value in R and hence no point of minimum value of f in R

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204.

Find the maximum and the minimum values, if there be any, of f given by f(x) = x, x ∊ (0, 1).

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205.

Without using derivatives, find the maximum or minimum value of the function 9x²+ 12x + 2.

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206.

Find the maximum and minimum values, if any, of the following function without using the derivatives:
9x² – 12x + 4

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207.

Find the maximum and minimum values, if any, of the following function without using the derivatives:
4x ²+ 28x + 49

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208.

Find the maximum and minimum values, if any, of the following function without using the derivatives:
x + 1, x ∊ (– 1, 1)

92 Views

209.

Find the maximum and minimum values, if any, of the following functions without using the derivatives:
x²

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210.

Find the maximum and minimum values, if any, of the following functions without using the derivatives:
– (x – 2 )² + 4

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