Question 1 Atte 1 pts OM Suppose that the differentiable function y= f(x) has an inverse and that the graph of f passes through the point (-1 , 3) with slope -= there. df-1 1. What is the value of at x=-1 ? [ Select ] [ Select ] dx 2 df- 1 2. What is the value of [ Select ] -2 at x=3 ? dx 1/2 -1/2 There is not enough information given to answer this question.\fQuestion 3 1 pts Find the equation of the tangent line to the graph of g(x) =2*-2x In 2+1 at x=0. Oy= (-In 2)x O y = 2x In 2 O y = (- In 2)x + 2 O y = (In 2)x+2 O y = In(2x)Question 4 1 pts The function f(x)=x+3x+6 is one-to-one. Find (f~])'(10). Provide your answer in decimal form, rounded to three decimals.Question 5 1 pts Find the equation of the line that is tangent to the curve y = x at the point (2 , 4) . Show and explain your work. Hint: Use logarithmic and implicit differentiation. That is, apply In() to both sides of the equation, and then differentiate with respect to x. Upload Choose a FileQuestion 6 1 pts sin (ath) -sin (a) How many values of a are there such that lim =4 ? h-0 h (Hint: What does the limit on the right represent?) Your answer should be an integer.Question 7 1 pts tan1(2):} if x20 ax+b if xvi' Let f(x}={ For which values of a and b is x) differentiable for every real number? 0 a can be anything; b= . Q a=2 ; b can be anything. Q 3:2: b=. Q a=: 5:2. Question 8 1 pts If g is a function satisfying 3(3}=g'r{3}=-2. and h[1)=tan_1[g{x}] , then what is i113)? Enter your answer as a decimal number. rounded to two decimal points. Question 9 1 pts There are exactly two points on the curve y=tan" (x) that have a tangent line with slope 91- (a) Find the distance between these two points. (b) Find the equation of the line which connects these two points. (c) What is the average rate of change of the function f(x)=tan (x) between these two points? (d) At which point(s) on the curve y=tan" (x) is the slope of the tangent line to the curve largest? Upload Choose a File