MATH 184 Lecture Notes - Lecture 7: Demand Curve

ool Careruly. maRe sure you are answering the que correctly I) y =x" + 2x Find where the slope of a tangent line is equal to 3 2) Differentiate each of the following functions a) y =-6x-4 2) Determine if the function has any horizontal tangent lines b) g(x)-re2x c) y=x2/3-74/3 3 24X 2 r +1 2 y = 2-x3 3) Use the quotient rule to show that the derivative of y = sec θ is y' = sec θ tan θ 4) Find the derivative only three of the following functions. Simplify each answer as mu possible a) f(x)=x' cos x b) f(x)= b) f(x)= 4x-21 y=ln(x5) c) -7 4t +5 e)y3x21 f) g(x)=cos(x3+4)

3. Find the first, the second and the third derivatives of: (a) f(x) = 1 / (8x+5) (b) g(x) = cos3x 4. Given the implicit relation: x^2+ y^2 - 16x - 12y = 0 . They let you know that the graph of this relation is a circle. (a) Let C (h, k) be the center and R be the radius of the circle. Write the given implicit relation under the standard form (x - h)^2 + (y - k)^2 = R^2 (b) Sketch the circle. (e) Find the slope of the circle at point B (0, 12) (d) Find the equation of the tangent line to the circle at B.

dition.pdf In Exercises 11-16, use the Chain Rule to evaluate the partial derivative at the point specified 11, af/du and af/du at (u. u) = (-1,-1), where f(x, y, z) = x3 + 12. df/as at (r, s) = (1,0), where f(x,y)=ln(xy), x = 3r + 2s, y=5r + 3s ms g(x,y)=1/(x+y2), (r. θ)=(2V2,5), r sin θ where 13, ag/ae at x r cos θ, y x2-y2. x = 52 + 1, y = 1- 14. ag/as at s = 4, where gir, y) 2s 15, ag/au at (u, u) = (0, l ), where g(x, y) =エ2-y2, x = e" cos t, 16. dh at (q, r) = (3. 2), where h(u, u) “c". “ = q3.-gr2 dg 17. A baseball player hits the ball and then runs down the first base line at 20 fus. The first baseman fields the ball and then runs toward first base along the second base line at 18 fus as in Figure 7 Lectue P13 Sidepp