Calculus

Differentiability

Characteristics of graphs of f and f'

         

Given f(x)=x2+9x+k,f'(x) = x^2 + 9x + k, if f(x)f(x) is an increasing function for all values of x,x, what is the range of k?k?

Suppose f(x)f(x) is a function such that y=f(x)y=f'(x) is given by the curve in the above diagram. If y=f(x)y= f'(x) is tangent to the xx-axis at x=a=7,x=a=7, which of the following statements is NOT correct about f(x)?f(x)?

Suppose f(x)f(x) is a differentiable function such that the graph of y=f(x)y=f'(x) is as shown in the above diagram. If a=2,b=3,c=5,d=7,a = 2, b = 3, c = 5, d= 7, and f(e)=f(d)f'(e) = f'(d) for all ed,e \geq d, which of following statements is correct?

Suppose f(x)f(x) is a function such that the graph of y=f(x)y=f'(x) is a line as shown in the above diagram. If a=19,a=19, which of following statements is correct?

Suppose f(x)f(x) is a function such that f(x)=K(xa)(xb),f'(x) = K(x-a)(x-b) , where KK is a positive constant. If a=5a=5 and b=10,b=10, which of following statements is NOT correct?

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