Define a quadratic function f(x)=7.6x^2+5.3x+2.7 for all positive x. Denote f'(x) to be the derivative of f(x). What is the value of f'(2)?
Question
Define a quadratic function f(x)=7.6x^2+5.3x+2.7 for all positive x.
Denote f'(x) to be the derivative of f(x).
What is the value of f'(2)?
Solution
To find the value of f'(2), we first need to find the derivative of the function f(x) = 7.6x^2 + 5.3x + 2.7.
The derivative of a function is found using the power rule, which states that the derivative of x^n is n*x^(n-1).
Applying the power rule to each term in the function:
- The derivative of 7.6x^2 is 2*7.6x = 15.2x.
- The derivative of 5.3x is 5.3.
- The derivative of a constant, like 2.7, is 0.
So, the derivative of the function f(x), or f'(x), is 15.2x + 5.3.
To find the value of f'(2), we substitute x = 2 into the derivative:
f'(2) = 15.2*2 + 5.3 = 30.4 + 5.3 = 35.7.
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