if f (x) = `x^4-62x^2+ax+9` attains its local maximum value at x= 1, find the value of a

if f(x)={(x^2,xle1),(ax+b,x>1):} is differentiable at x = 1, find the values of a and b. Hence find f'(1)

If u_x = e^(ax) ,find the value of Deltae^(ax)

If 5x + 7 le 3x + 9 , find the maximum value of x

if f (x) = x^3 , show that f''(x) exist for all real values of x and find it.

If Var(x) = 4, Find the value of Var (3x + 2).

If x-y=7 and xy=9, then find the value of (x^2+y^2)

If f(x)=logx,find the value of Delta logx.

If one zero of the polynomial (a^2 + 9)x^2 + 13x + 6a is reciprocal of the other, find the value of a .

If abs[[x+2,3],[x+5,4]]=3 , find the value of x.

If f(x) = k, a constant, find the value of Deltaf(x) .