The absolute extrema of a function are the largest and smallest y-values of the function on a given domain. This domain may be given to us (as in this problem) or it might be the domain of the function …

(dy)/ (dx)= (cos^2t-tsin2t)/ (2t-cost+tsint) To find derivative of a parmetric equation such as f (t)= (x (t),y (t)), we use formula (dy)/ (dx)= ( (dy)/ (dt))/ ( (dx ...

Jan 24, 2016 · Explanation: Find the value of the second derivative at #x=-2#, since the sign second derivative determines the concavity or convexity of a function.

Jan 15, 2016 · To find the second derivative of the function, first simplify #f (x)#.

Oct 21, 2017 · The derivative of the function at x= 1/4 will be (1/4, -4). We can immediately write the function as f (x) = x^ (-1/2) Then we can find the derivative using the power ...

This means that is may be a point of inflection. We can check a graph of the function: graph {-5x^5-2x^4-2x^3+14x-17 [-2.5, 2.5, -120, 100]} Graphically, x=0 does appear to be a point of inflection (the …

dy/dx= (x^2-6x+4)/ (x-3)^2 We want to find the derivative of y= (x^2-4)/ (x-3) Use the quotient rule, if y=f/g then dy/dx= (f'*g-f*g')/g^2, thus f=x^2-4=>f'=2x g=x-3 ...

Explanation: what you are looking for is the instantaneous gradient at #x=1#. To do so, you must find the derivative of the function, and substitute the #x=1# into the derivative to find the gradient.

Explanation: To test a function's concavity or convexity, find the value of the second derivative of the function at a point:

The linear function y=30x+25 represents the total weight y (in pounds) of the wagon and its contents after you have loaded x blocks? What is the derivative of ln(x2 +1 2x)? What are the critical points of …