36- 32 28- 24 20 16- 12 -4 -2 -1 For the above function f( x ) = 7 - 0.65², estimate f'(x) using h = 0.001 for the following three valu f'( – 3.75) - f'(0.5) = f'(1.75) -
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- Consider the function f(x)=ln (1+x2). a. Find all the critical values of f(x)=ln (1+x2). Using the first derivative test, identify the intervals of increase and intervals of decreaseLet h be the function h(x) = 2x2. The value of x decreases as x changes from −2 to −1. TRUE OR FALSE As x changes from −2 to −1, h(x) changes from .... to .... As x changes from −1 to 1, h(x) changes from .... to .... 4. The average rate of change of h on the interval from −1 to 1 is greater than the average rate of change of h on the interval from −2 to −1. TRUE OR FALSE? Justify by calculating both average rates of change. Show all work. 5. Mark the correct answer. h(x) is concave up. concave down. neither. both PLEASE HELP ME WITH THEM ALL. THANK YOUUA 100-gal tank initially contains 25% dye solution. A 40% dye solution is allowed to enter at a rate of 10 gal/min and the resulting uniform mixture is removed from the tank at the same rate. Derive an expression for the amount of dye in the tank as a function of time. Find the time t at which the tank contains 26% dye solution.
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- The derivative of ƒ(x) = x2 is zero at x = 0, but ƒ is not a con-stant function. Doesn’t this contradict the corollary of the Mean Value Theorem that says that functions with zero derivatives are constant? Give reasons for your answer.Shows that if a function f(x) is continuous in interval [a,b] then most likely the derivative of f(x) is also continuous at interval [a,b]How can we use the derivative f'(x) of a function f(x) to determine where the local max(s) and min(s) are and what the intervals of increasing and decreasing are?