Let `f(x)=ax^(2)+bx+c,`if `a>0` then `f(x)` has minimum value at x=

Theorem: Let f(x)=ax^(2)+bx+c be a quadratic function. If a gt0 then f(x) has minimum value at x=(-b)/(2a) and the minimum value =(4ac-b^(2))/(4a) .

Theorem : Let f(x)=ax^(2)+bx+c be a quadratic function. If a gt 0 then f(x) has minimum value at x =(-b)/(2a) and the minimum value = (4ac -b^(2))/(4a)

Theorem : Let f(x)=ax^(2)+bx+c be a quadratic function. If a lt 0 then f(x) has maximum value at x=(-b)/(2a) and the maximum value =(4ac-b^(2))/(4a)

Theorem: Let f(x)=ax^(2)+bx+c be a quadratic function. If a lt 0 then f(x) has maximum value at x=(-b)/(2a) and the maximum value =(4ac-b^(2))/(4a)

Consider the polynomial f(x)=ax^(2)+bx+c. If f(0),f(2)=2 then the minimum value of int_(0)^(2)|f'(x)dx is

Let f(x) = ax^(3) + bx +c . Then when f is odd,

Let f(x0=(1+b^(2))x^(2)+2bx+1 and let m(b) be the minimum value of f(x). As b varies, the range of m(b) is

If f(x)=be^(ax)+ae^(bx) , then f" (0) =