Prove that `f(x)=a x+b` , where `a ,\ b` are constants and `a<0` is a decreasing function on `R` .

A function has the form f(x)=ax+b, where a and b are constants. If f(2)=1" and "f(-3)=11 , the function is defined by

Let f(x)=a x^2-b|x|, where aa n db are constants. Then at x=0,f(x) has a maxima whenever a >0,b >0 a maxima whenever a >0,b 0,b 0, b<0

The graphs shown above represent f(x) and f(x+a) + b, where a and b are constants. Which of the following is the ordered pair (a,b) ?

Let f(x)=a+b|x|+c|x|^4 , where a , ba n dc are real constants. Then, f(x) is differentiable at x=0, if a=0 (b) b=0 (c) c=0 (d) none of these

The potential in the electric field varies as V = -a x^2 + b with respect to x - coordinate, where a and b are constants. Find the charge density rho (x) in a space.

Form the differential equation of y=a(x+b) , where a,b are constants.

Let f(x)=a+b|x|+c|x|^(2) , where a,b,c are real constants. The, f'(0) exists if

Suppose f(x) is a function satisfying the following conditions: f(0)=2,f(1)=1 f has a minimum value at x=5/2 For all x ,f^(prime)(x)=|2a x2a x-1 2a x+b+1bb+1-1 2(a x+b)2a x+2b+1 2a x+b| where a , b are some constants. Determine the constants a , b , and the function f(x)

Suppose f(x) is a function satisfying the following conditions: f(0)=2,f(1)=1 f has a minimum value at x=5/2 For all x ,f^(prime)(x)=|2a x2a x-1 2a x+b+1bb+1-1 2(a x+b)2a x+2b+1 2a x+b| where a , b are some constants. Determine the constants a , b , and the function f(x)

If f(a-x)=f(a+x) " and " f(b-x)=f(b+x) for all real x, where a, b (a gt b gt 0) are constants, then prove that f(x) is a periodic function.