For what values of a and b is the line 6x + y = b tangent to the graph of y ax' when x = 2? Report only the value of b. Show your work in the PDF version of the test.
Find the equation of the tangent line to the graph y=x√ at x=4. y = On graph paper, sketch the graph and the tangent line using the x-values 3.5,4,4.5. The tangent line provides a linear approximation to x√ near x=4. Use this approximation to find approximate values for 4.5‾‾‾√ and 5√
Problem #8: Find the two values of x at which the graph of the given function has a horizontal tangent line. (If there is only one value of x then enter it twice, e.g., 12,12) (a) y - (x - 3)(x2 - 6x +9)
5. Find the e-coordinate of the point on the curve : +3y3 = 3ay where the tangent is horizontal. Show your work in the PDF version of the test. 7. How many real roots does the equation ! 9x +c=0 have in the interval (-3,0? Hint: use the Mean Value Theorem (Rolle's Theorem). Show your work in the PDF version of the test. A. At most two real roots B. At least one real roots C. No real roots D....
a) b) 8. Using Graph paper, graph the following functions: y = 2cos(2x) for values of x = -11, -11/2, -11/6, -11/4, -1/3, y =tan( x + 11/2) + 1. For the same values of x as above. Provide your work on graph paper!! 112, -11/6, -11/4, -1V/3, 0, 1/3,1/4, 1/6,112, 11, 311/2 Section II: Vectors in Mechanics (5 points): Show your work!! 1. The vector A has a magnitude of 7.25 m. Find its components for direction angles of:...
0 intersect only at (0,0) g(r)at z arctan(3z) Show that the graph y f(x) and its tangent line y po Consider the ftunction f(x) Intermediate steps: 1) The lIne tangent to y f(x)atz -0isy g(x) where g(r) 9(a)- 2Let H(x) f(x) - 9(x) The derivative ot H (x)s H'(z) = which is zero only when x = Rolle's theorem to H (x) on the interval [ri, 0]. Get a contradiction. 4) Now assume that we have zp O where f(2)-9(T2)...
Q3 (Show your work!) 25 Points Let • f(x) = a - (x + b), where a, b and care constants • the graph of y = f(x) has a vertical tangent line at its inflection point (1,2) the tangent line to the graph of y = f'(x) at x = 2 is perpendicular to the tangent line to the graph of y = e-sin at x = 0 Find the values of a, b and c and sketch the...
b What values of a and b maximize the value of ( ( 6x-x²) dx? a (Hint: Where is the integrand positive?) a= and b= maximize the given integral. (Simplify your answer. Type a whole number.)
(1 point) For what values of x is the tangent line of the graph of f(x) = 10x? - 45x? +61x + 30 parallel to the line y = x -0.5?
please explain how you do part (b) clearly.
Given the curve x-t5, y--t+4t +3, find the exact values: 18) a) of the coordinates of the leftmost point on the curve. (Use Calculus and show your work). b) of the parameter t where the graph crosses itself. (Use any method you wish - but show your work). c) of the parameter t where the slope of tangent line to the curve is(Use Calculus and show your work).