1024worksheet6

1024worksheet6 - (a f x = e π x π π x(b g x = e x π-e...

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Polytechnic Institute of NYU MA 1024/1324 Worksheet 6 Print Name: Signature: ID #: Instructor/Section: Directions: Show all your work for every problem. Problem Possible Points 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 10 Total 100 1
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2 (1) Where are the following functions not differentiable? (a) (b)
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3 (2) (a) Let f ( x ) = ± x 2 - x, x 2 2 x - 2 , x > 2 (i) Is f ( x ) continuous at 2? (ii) Is f ( x ) differentiable at 2? (b) Let f ( x ) = ± 1 - x 2 , x 0 x 2 , x > 0 (i) Is f ( x ) continuous at 0? (ii) Is f ( x ) differentiable at 0?
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4 (3) Graph the function defined by h ( r ) = 1 + cos ± πr 3 ² , - 6 r 6 2 , r < - 6 0 , r > 6 (a) At what points is h ( r ) not continuous (if any)? (b) At what points is h ( r ) not differentiable (if any)?
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5 (4) Find the derivatives of the given functions in respect to x : (a) F ( x ) = 11 x 5 - 6 x 3 + 8 (b) F ( x ) = ( x - 1) ( x - 2) (c) h ( x ) = t e (d) g ( x ) = x - 1 + x 4 / 3 + x - 1 / 2
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6 (5) Find A and B given that the derivative of f ( x ) = ± Ax 3 + Bx + 2 , x 2 Bx 2 - A, x > 2 is continuous for all x .
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7 (6) Find C and D given that the derivative of g ( x ) = ± Cx 2 + D,x < - 1 Dx 5 + Cx + 4 ,x ≥ - 1 is continuous for all x .
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8 (7) Find the derivatives of the given functions.
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Unformatted text preview: (a) f ( x ) = e π + x π + π x (b) g ( x ) = e x + π-e x-π (c) h ( x ) = ln (6) · 6 x + 6 · (ln 6) x (d) y ( x ) = 2 e + x + 3 x + 4 x-e 9 (8) Let r ( t ) = 2 t 6 + 5 t 5-9 x 2 + 4 + 3 e x (a) What is dr dt ? (b) What is dr dx ? (c) What is the seventh derivative of r in respect to t ? (d) What is the sixth derivative of r in respect to t ? 10 (9) Let h ( x ) = e-e x (a) Find the slope of h ( x ) at the point where it crosses the x-axis. (b) Find the equation of the tangent line to the curve at this point. (c) Find the equation of the line perpendicular to the tangent line at this point. 11 (10) Determine the coefficients A , B , C so that the curve f ( x ) = Ax 2 + Bx + C will pass through the point (1 , 3) and be tangent to the line 4 x + y = 8 at the point (2 , 0)....
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This note was uploaded on 12/09/2009 for the course MA 1024/1324 taught by Professor N/a during the Spring '09 term at NYU Poly.

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1024worksheet6 - (a f x = e π x π π x(b g x = e x π-e...

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