MATHEMATICS

JAMB 2000 - Question 39

Mathematics 2000 JAMB Past Questions - Question 39: A function f(x) passes through the origin and its first derivative is 3x+2.what is f(x)?

A function f(x) passes through the origin and its first derivative is 3x+2.what is f(x)?
A:
B:
C:
D:
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Correct Answer

A

Explanation

dy/dx = 3x +2dy = (3x +2) dxy = 3x/2 +2x +corigin (0,0) (x,y)x = 0, y = 0therefore C = 0y = 3xsup 2 +2x A function f(x) passes through the origin and its first derivative is 3x+2.what is f(x)? To find the function f(x), we need to integrate the first derivative of f(x), which is 3x + 2, with respect to x.Integrating 3x + 2, we get:∫(3x + 2) dx = (3/2)x² + 2x + CSince the function f(x) passes through the origin (0, 0), we can substitute x = 0 into the integrated expression to find the value of the constant C:(3/2)(0)² + 2(0) + C = 00 + 0 + C = 0C = 0Therefore, the function f(x) is given by:f(x) = (3/2)x² + 2xSo, f(x) = (3/2)x² + 2x.