Question

let f(x) be a polynomial. then the second order derivative of f(e^x) is?
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Answer 1

Answer:

i hope it will help you

Step-by-step explanation:

Let f(x)=px

2

+qx+r

Differentiatin g w.r. to x, we get

f

′

(x)=2px+q

Now,

f(−1)=f(1)

∴p−q+r=p+q+r

∴q=0

∴f

′

(x)=2px

f

′

(a)=2pa.f

′

(b)=2pb,f

′

(c)=2pc

Since a,b,c are in A.P., therefore

2b=a+c

4pb=2pa+2pc

2f

′

(b)=f

′

(a)+f

′

(c)

∴f

′

(a),f

′

(b),f

′

(c) are in A.P