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Derivative of One Function w.r.t Another

5. Find the v...

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5. Find the value of p and q so that the given function is differentiable at x=1

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Q. Find the values of

a

b

so that the function

f (x) = {\begin{matrix} x^{2} + 3 x + a, & i f & x \leq 1 b x + 2, & i f & x > 1 \end{matrix}

is differentiable at each

x \in R

Q. Find the values of a and b so that the function

f (x) \{\begin{cases} x^{2} + 3 x + a, & if x \leq 1 \\ b x + 2, & if x > 1 \end{cases}

is differentiable at each x ∈ R.

Q. Find the values of a and b so that the function f given by

f (x) = \{\begin{matrix} 1, & i f x \leq 3 \\ a x + b, & i f 3 < x < 5 \\ 7, & i f x \geq 5 \end{matrix}

is continuous at x = 3 and x = 5.

Q. Find the value f(0) so that the function

f (x) = \frac{1}{x} - \frac{2}{e^{2 x} - 1}, x \neq 0

is continuous at

x = 0

& examine the differentiability of f(x) at

x = 0

f

is differentiable function satisfying

f (0) = 0

g (x) = \frac{f (x)}{x}

, then value, that should be assigned to

g (0)

g

is continuous at

0

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