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Calculus I Week 04 (Quiz 04) Problem Bank 5. Quiz 04 will be administered in recitation during Week 04. Two questions chosen at random will be selected for the 6 quiz. The actual quiz questions will be variants of these practice quiz questions. In other words, the same concepts will be addressed, but numbers, expressions, or specific questions asked may differ. 7. The tangent line reveals two things about ght} at x = 3. Use those things to find g[3} and 9T3]. Find h'Tx] and plug in x = 1 to get the second equation of a system. . To be differentiable at x = 4, x} needs to be both continuous and not have a sharp "corner". Those are two conditions and we have two unknowns. 1. Find the value(s) of x such that the graph of the 16 8. We need to get to the second derivative of this function x} 2 x2 + x2 has a horizontal tangent line. quotient. Simplify as you go. _ I I 9. Two lines are perpendicular if the product of their 2. Let {[x] = x _ a' F1nd the value of 0. so that f [I] = a. slopes is I. 3. Determine the value x for which 10. Recall that 16% = ( W)" = h [xu] f [x] : x3 9x2 + 5x :37 has the fewest instantaneous rate of change; also give the instantaneous rate of change at that point. M th 165 ' 04 fi 1 4. For what value of x does the graph of the function a Quiz na answers f[x} = x2 3x have a horizontal tangent line? 1 x _ :|:2 x} , _ 5. Suppose that h[x] = 3x" h [1] = 2, and 2. 0. _ 1 3f'[I] f[l] = 31. Find the values of f'(l] and 3_ _22 at x = 3 f[1 }. 4 _ a 6. Let y : x] be a function that is differentiable at all ' x _ 2 real numbers. Suppose f has the form: 5 f'll] _ 8 f[]} _ _7 f[ ] cxz b if x g 4 ' X : 2\/)_c+c ifx>4 6.b=andc=] Find the values of b and c. 16 16 . . 7 y = 3x 5 7. leen that y = 51x 1 '17 1s tangent to y = ngfx} at x = 3, find the tangent line to y 2 90] at x = 3. 8 A. _l_ ' _ 2 x2 + A _ 8. Suppose that {(x] = x where A Is a constant. 9 'I T . 0. : 5 If f"[2] = l, find the value of A. 8 10 A. E 9. Let L1 be the secant line to the graph of y = x2 x + 8 I 9 through the two points where x = 3 and x = 0.. Let L; be the line tangent to the graph of y = x2 x + 8 at x = 3. Find the value of the constant 0. so the lines LT and L; are perpendicular. 10. Let f[t] = . Find A such that f'U't] = 27. 2 u'tl Math 165 Quiz 04 hints 1. What is the slope of a horizontal line? 1 4. 3. What happens to the tangent line at the lowest point? Not the lowest point of f [x], but the lowest point of the instantaneous rate ofchange of the}. 2. Find the derivative of {(74} at 1, then use that f'[1} = 4. What is the slope of a horizontal line? What is the slope of a tangent line to the graph of the]