Question

If f(x)=9x⁴/² +25x²/⁵ , then f ′′ (x)=ax⁷ +bx⁴ , where a=p=b=q.

Answer 1

To find the second derivative of the function f(x) = 9x^4/2 + 25x^2/5, differentiate it twice using the power rule. The second derivative is 27x^1/2 - 6x^-8/5.

Step-by-step explanation:

To find the second derivative of the function f(x) = 9x^4/2 + 25x^2/5, we need to differentiate it twice.

First, let's find the first derivative of f(x).

Using the power rule of differentiation, we can differentiate each term separately:

• The derivative of 9x^4/2 is 18x^3/2.
• The derivative of 25x^2/5 is 10x^-3/5.

Now, let's find the second derivative.

Again, using the power rule, the derivative of 18x^3/2 is 27x^1/2, and the derivative of 10x^-3/5 is -6x^-8/5.

Therefore, f''(x) = 27x^1/2 - 6x^-8/5.