If g(x) is a continous function at x=a such that `g(a)gt0` and `f'(x)= g(x)(x^2-ax+a^2) " for all " x in K` then f(x) is

Options

A. increasing in the nieghbourhod of x=a
B. decreasing in the nieghbourhod of x=a
C. constant in the nieghbourhod of x=a
D. maximum at x=a

Answer

A

Explanation

Since g(x) is continuous at x=a and ` g(a)gt0 `
`therefore g(x)gt0` for all x belonging inn the neighbourhod of x=a
`rArr f'(x)gt0 ` for all x in the neighbourhood of x=a `[therefore x^2-ax+a^2gto " for all "x in R]
`rArr` f(x) is increasing in the nieghbourhood of x=a