Let f(x) be defined as f(x)={tan−1α−5x2,0<x<1and−6x,x≥1 if f(x) has a maximum at x=1, then find the values of α .

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Question

Let $f (x)$ be defined as $f (x) = {tan^{- 1} α - 5 x^{2}, 0 < x < 1 and - 6 x, x \geq 1$ if $f (x)$ has a maximum at $x = 1,$ then find the values of $α$ .

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Let

f (x)

be defined as

f (x) = {tan^{- 1} α - 5 x^{2}, 0 < x < 1 and - 6 x, x \geq 1

f (x)

has a maximum at

x = 1,

then find the values of

α

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Question Text

Let

f (x)

be defined as

f (x) = {tan^{- 1} α - 5 x^{2}, 0 < x < 1 and - 6 x, x \geq 1

f (x)

has a maximum at

x = 1,

then find the values of

α