Write True/False:
If f'( c )=0 then f(x) has a local maximum or a local minimum at x=c

Write True/False: If f'( c ) exists and f'( c )gt0 , then f(x) has a local minimum at x=c.

Let f(x) be a polynomial of degree 3 such that f(-2)=5, f(2)=-3, f'(x) has a critical point at x = -2 and f''(x) has a critical point at x = 2. Then f(x) has a local maxima at x = a and local minimum at x = b. Then find b-a.

Consider the function f:(-oo,oo)vec(-oo,oo) defined by f(x)=(x^2+a)/(x^2+a),a >0, which of the following is not true? maximum value of f is not attained even though f is bounded. f(x) is increasing on (0,oo) and has minimum at ,=0 f(x) is decreasing on (-oo,0) and has minimum at x=0. f(x) is increasing on (-oo,oo) and has neither a local maximum nor a local minimum at x=0.

Find the values of x, if any, for which f(x) has local maximum and local minimum when f(x)=sinx+cosx, x in [0, 2pi]

Find the values of x, if any, for which f(x) has local maximum and local minimum when f(x)=5x^6-18x^5+15x^4-10

Write True/False: If f(x) has an absolute maximum at x=c, then f'( c )=0

Let f(x)={(1+sin(x), if x lt 0), (x^2-x+1, if x >= 0):}, then: (a) f has local maximum at x=0, (b). f has local minimum at x=0, (c) f is increasing everywhere, (d) f is decreasing everywhere.

Let f(x)=x^(3)+ax^(2)+bx+c , where a, b, c are real numbers. If f(x) has a local minimum at x = 1 and a local maximum at x=-1/3 and f(2)=0 , then int_(-1)^(1) f(x) dx equals-