Question

If f(x) = ear? +bx+c the f'(x) is​

Answer 1

Answer:

Step-by-step explanation:

If f(x)=ax^2+bx+c & f(x+1)=f(x)+x+1 is an identity, what are the values of a & b?

Given, f(x) = a(x^2) + bx + c.

So, f(x + 1) = a * {(x + 1)^2} + b * (x + 1) + c

= a(x^2) + 2ax + a + bx + b + c

= {a(x^2) + bx + c} + (2ax + a + b).

= f(x) + (2ax + a + b).

But, it is given, f(x + 1) = f(x) + (x + 1).

So, if we match the respective coefficients, we can say:

a + b = 1 and 2a = 1 which gives a = (1 / 2).

So, a = (1 / 2) and b = (1 / 2).

Answer 2

Answer:

Answer in attachment...