If f(x)=-3x+2,x<112x2+7,x≥1, then which of the following is not true

f'(X)=−3, if x<1 x, if x≥1⇒f1(1−)=−3,f1(1+)=1

If f(x)=-3x+2,x<112x2+7,x≥1, then which of the following is not true

f'(X)=−3, if x<1 x, if x≥1⇒f1(1−)=−3,f1(1+)=1

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$If f (x) = \{\begin{cases} - 3 x + 2, x < 1 \\ \frac{1}{2} x^{2} + 7, x \geq 1, \end{cases} then which of the following is not true$

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$f' (1 +) = 1$

$f' (1 -) = - 3$

$f' (1 -) = f' (1 +) = 1$

$f is not differentiable at x = 1$

answer is C.

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Detailed Solution

$f' (X) = \{\begin{cases} - 3, i f x < 1 \\ x, i f x \geq 1 \end{cases}$

$\Rightarrow f^{1} (1^{-}) = - 3, f^{1} (1^{+}) = 1$

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If f(x)=-3x+2,x<112x2+7,x≥1, then which of the following is not true

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$If f (x) = \{\begin{cases} - 3 x + 2, x < 1 \\ \frac{1}{2} x^{2} + 7, x \geq 1, \end{cases} then which of the following is not true$