Another Calculus

Sorry I have been trying to figure this out all day. Find the largest and smallest values of the given function over the prescribed closed, bounded interval.
g(t)= (t^3/2)(e^-2t) for 0<t<1.

  1. 👍 0
  2. 👎 0
  3. 👁 82
asked by Carly
  1. Using the product rule
    g'(t) = t^(3/2)(-2)e^(-2t) + (3/2)t^(1/2)(e^(-2t))
    common factor ...
    = (1/2)e^(-2t)(t^(1/2)) [-4t + 3}

    set this equal to zero
    from the first factor we get t=0
    and from the second one we get t = 3/4

    now evaluate
    g(0) = ..
    g(3/4) = ..
    g(1) = ...

    and determine which is the largest and smallest value.

    1. 👍 0
    2. 👎 0
    posted by Reiny

Respond to this Question

First Name

Your Response

Similar Questions

  1. Chemistry

    Which response presents ions in order of increasing atomic radius? a) smallest Cl-, K+, Na+ largest b) smallest Cl-, Na+, K+ largest c) smallest K+, Na+, Cl- largest d) smallest Na+, K+, Cl- largest I would assume the answer would

    asked by Anonymous on May 7, 2017
  2. Chem21

    Rank these gases in order of increasing standard molar entropy: Column preview Smallest S Br2(g) Second smallest S F2(g) Second largest S I2(g) Largest S Cl2(g) Matching pairs Smallest S Second smallest S Second largest S Largest

    asked by Ryan on May 2, 2011
  3. Chemistry

    Doing some homework, are my answers right? HCN= Polar HCOOH= Polar H2CCCH2= Nonpolar Out of the following elements: Na, H, and Au order them least to greatest in the following: Eletronegativity= Na is smallest, H is second, Au is

    asked by Matthew on April 3, 2014
  4. precalculus

    Use the elimination method to find all solutions of the system of equations. (Order your answers from smallest to largest x, then from smallest to largest y.) x − y2 + = 0 2x2+ y2 −9 = 0

    asked by Ama on November 4, 2012
  5. precalculus

    Find all solutions of the system of equations. Order your answers from smallest to largest x, then from smallest to largest y.) x^2 + y2= 53 x2− y2= 3

    asked by amaa on December 1, 2012
  6. Math - Exponential

    Please check if my answers are correct! Thank you. Differentiate f(t) = √(36 ln(t) + 5t) f'(t) = (1/2) * (36 ln(t) + 5t)^-1/2 * (36/t + 5) f'(t) = (1/2)* (36/t + 5)/((36 ln(t) + 5t)^1/2 f'(t) = (36 + 5t) / (2t √(36lnt + 5t))

    asked by Anonymous on January 17, 2009
  7. Math

    Consider two nonnegative numbers x and y such that x + y = 12. Find the values of x and y that optimize the following quantity. xy Maximize the quantity. {x, y} = Minimize the quantity. (Order your answers from smallest to largest

    asked by Meghan on April 7, 2018
  8. intermediate algebra

    A triangle is such that the largest angle is 11 times the smallest angle. The third angle is 27° less than the largest angle. Find the measure of each angle. (Enter solutions from smallest to largest.)

    asked by jess on February 5, 2012
  9. intermediate algebra

    A triangle is such that the largest angle is 11 times the smallest angle. The third angle is 27° less than the largest angle. Find the measure of each angle. (Enter solutions from smallest to largest.)

    asked by sally on February 5, 2012
  10. algebra

    Identify the vertices of the solution region of the system of linear inequalities. (Order your answers from smallest to largest x, then from smallest to largest y.) x ≥ −2 x ≤ 3 y ≤ 5 y ≥ x (x, y) = (x, y) = (x, y) = (x,

    asked by Abby on December 4, 2014

More Similar Questions