Question

If for $\rm f(x)=\lambda x^{2}+\mu x+12$, $\rm f'(4) = 15$ and $\rm f'(2)=11$, then find λ and μ.

Answer 1

Kia hai ya Bhai chamaj ma Nahi aia

Answer 2

Answer:

λ = 1

and,

μ = 7

Step-by-step explanation:

In the question,

We have a function,

$f(x)=\lambda x^{2}+\mu x+12$

Now, We also have been provided that,

f'(4) = 15 (Given)

and,

f'(2) = 11 (Given)

So, on differentiating the function f(x) w.r.t 'x' we get,

$f(x)=\lambda x^{2}+\mu x+12\\\frac{d}{dx}f(x)=2\lambda x+\mu \\f'(x)=2\lambda x+\mu$

Now,

On checking the value of f'(x) at x = 4, we get,

$f'(x)=2\lambda x+\mu \\15=2\lambda (4)+\mu \\15=8\lambda+\mu .........(1)$

Now, value of f'(x) at x = 2, we get,

$f'(x)=2\lambda x+\mu \\11=2\lambda (2)+\mu \\11=4\lambda+\mu .........(2)$

Now, on solving the equation (1) and (2) simultaneously we get,

$\lambda = 1\\And,\\\mu = 7$

Hence, the required values are,

λ = 1

and,

μ = 7