Let f and g be two twice differentiable functions defined form R → R. If f (x) has a local maximum at x = c and g(x) has a local minimum at x = c, then*

Consider the function and fill in the spaces below.  By the First derivative test, the function has:a local maximum at the point Answer 1 Question 7, Answer 2 Question 7 and a local minimum at the point

Let g:R→R be a non constant twice differentiable such that g′(12)=g′(32). If a real valued function f is defined as f(x)=12[g(x)+g(2−x)], thenf′′(x)=0 for atleast two x in (0,2)f′′(x)=0 for exactly one x in (0,1)f′′(x)=0 for no x in (0,1)f′(32)+f′(12)=1

At any x, if first order and second order derivatives of a function f is equal to 0 and greater than 0 respectively, then1 pointx is a local maximum of fx is a local minimum ofx is a stationary pointNone of the above

Let f(x) be a real value function such that f(x)=2x−1x−2∀ x ∈ (2,∞) and g(x)=x2+1x+(f(x))2+1f(x)∀ x>2, then minimum value of g(x) is

Consider the polynomial function g(x) = 2x^4 - 5x^3 + 3x^2 - 2x + 1.a.It has a local minima at 1.65b.It has a local maxima at 1.65c.It has no maxima or minimad.It has no critical points