If f(x)=logb(x),b>0,b=1, what is f′(x) ? f′(x)=x1 f′(x)=xlnb1 f′(x)=logδ(x)1 f′(x)=xlogb1 Question 17 If f(x)=bx,
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Let h(x)=x3+1. Identify the functions f(x) and g(x) such that h(x)=f(g(x)). f(x)=x+1,g(x)=x3f(x)=x3+1,g(x)=xf(x)=x3,g(x)=x+1f(x)=x,g(x)=x3+1 Question 14 Let f and g be differentiable functions of x. What is the derivative of f(g(x)) ? f′(x)g′(x) f(g)g′(x) f′(g)g(x)+g′(x)f(g) f′(g)g′(x)
If f and g are differentiable functions of x, what is the derivative of g(x)f(x) ? g′(x)∣2f′(x)g(x)−g′(x)f(x)g(x)]2f′(x)g(x)−g′(x)f(x)g(x)∣2f′(x)g(x)+g′(x)f(x)g(x)f′(x)g(x)−g′(x)f(x) Question 13 Let h(x)=x3+1. Identify the functions f(x) and g(x) such that h(x)=f(g(x)). f(x)=x+1,g(x)=x3f(x)=x3+1,g(x)=x
Let C(x)=2x+30 and R(x)=10x. Find the marginal profit function. P(x)=8x−30 P′(x)=8 P′(x)=8x P(x)=8x+30 Question 10 Suppose the marginal profit from producing and selling 50 coffees is P′(50)=$1.50. Interpret the value $1.50. When 50 coffees are produced and sold, maximum profit is $1.50 When 50 coffees are produced and sold, profit is increasing at a rate of $1.50 per additional coffee When 50 coffees are produced and sold, each of the 50 coffees makes a profit of $1.50 When 50 coffees are produced and sold, each coffee cost $1.50
What is the definition of the derivative of the function f at a point x=a ? the instantaneous rate of change of f(x) at all x the instantaneous rate of change of f at x=a the slope of the secant line the average rate of change of f at x=a Question 3 When estimating a derivative, what should be the value you use for h? 0.1 0.01 0.001 0.0001