Test 4 sols

# Test 4 sols - TEST 4 SOLUTIONS 1[15 Find intercepts...

This preview shows pages 1–2. Sign up to view the full content.

TEST 4 SOLUTIONS 1.[15] Find intercepts. intervals on which f is increasing, decreasing; open intervals where f is concave up, concave down; and x-coordinates of all inflection points; also state which points [x- coordinates only] are stationary points, PONDS, and classify as relative maximum or minimum points; specify equation of any vertical tangent. DO NOT SKETCH ( 29 4/3 1/3 f x x x = - [SHOW SIGN GRAPHS AS USED IN CLASS FOR BOTH f and f ′′ ] ( 29 ( 29 4/3 1/3 1/3 1 f x x x x x = - = - so the intercepts are (0,0) and (1,0) ( 29 1/3 2/3 1/3 2/3 2/3 4 1 1 1 4 1 4 3 3 3 3 x f x x x x x x - - = - = - = so there is a POND at x = 0 and stationary point at x = ¼ and the the sign graph for f shows f is increasing on x > ¼, decreasing on x < ¼ [the denominator is always > 0] x = 0 has a vertical tangent there [the derivative doesn’t change sign there] so I guess I mislead you about that – sorry. x = ¼ is a minimum. [No vertical ( 29 2/3 5/3 2/3 5/3 5/3 4 2 2 2 1 2 1 9 9 9 9 x f x x x x x x - - + ′′ = + = + = and this changes sign at both x = 0 and x = - ½ So both these points are inflection points [since f is defined at both] A sign graph of f ′′ shows that f is concave down for -1/2 < x < 0 [ f ′′ < 0 there] and concave up for x < - ½ and x > 0 [ f ′′ > 0 for both of these] 2.[10]Find the absolute maximum and minimum values of ( 29 [ ] cos on / 2, f x x x π = + - Since f is continuous everywhere, the Extreme Value Theorem applies and we are guaranteed both an absolute maximum and an absolute minimum on the closed interval. All

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 12/26/2011 for the course MAC 2311 taught by Professor Staff during the Fall '08 term at FIU.

### Page1 / 5

Test 4 sols - TEST 4 SOLUTIONS 1[15 Find intercepts...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online