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

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 ) does not exist and f'(x) changes from positive to negative as x increases through c, then f(x) has a local minimum at x=c.

If f(c) lt 0 and f'(c) gt 0 , then at x = c , f (x) is -

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

If f'(x) changes from negative to positive at x_(0) while moving from left to right, i.e. f'(x)lt0,xltx_(0) f'(x)gt0,xgtx_(0), then f(x) has local minimum value at x=x_(0)

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

Let f and g be two differentiable functions defined from R->R^+. If f(x) has a local maximum at x = c and g(x) has a local minimum at x = c, then h(x) = f(x)/g(x) (A) has a local maximum at x = c (B) has a local minimum at x = c (C) is monotonic at x = c 1.a g(x) (D) has a point of inflection at x = c

Write True/False: If for any function y=f(x), f'( c )=0, then the tangent drawn to the curve at x=c is parallel to the y-axis.