SS_Mat135_T1

# Dx dx critical points the values of x domain of fx

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Unformatted text preview: unction Step 1. Take the derivative of both sides with respect to x. Use the Chain Rule on terms involving y (and note that the derivative of y with changes from negative to positive at p, then f has a relative minimum at p. If f ’ changes from positive to negative at p, then f has a relative maximum at p. Second derivative test: If f ′ p = 0 and dy dx .) Step 2. Collect all terms involving dy dx f ′′( p ) > 0 , then f respect to x must be left as on one side of the equation. Step 3. Solve for dy dx . EXAMPLE: 2 2 Differentiate the function x + xy + y = 7. SOLUTION: ⇒ ⇒ Recall that by definition, a curve is concave up when its second derivative is positive. We find: dy 2x = dx 3 + x 2 and f ’ () dx 2 = and 2( 3 + x 2 ) − 4 x 2 (3 + x 2 ) 2 = 6 − 2x 2 >0 (3 + x 2 )2 (when - 3 < x < 3 ) CURVE SKETCHING Step 1. Find the intercepts. Step 2. Find all the asymptotes. Step 3. Find...
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