Calculus - please help

posted by .

Can someone please do these questions step by step and explain them. I really need help so I can do the same for the rest.

a) f(x) = e^(sqrtx)
1. State the domain and range
2. Find f'(x)
3. Determine the intervals of increase and decrease.

d) f(x) = e^x + e^-x
1. State the domain and range
2. Find f'(x)
3. Determine the intervals of increase and decrease.

  • Calculus - please help -

    x must be positive if sqrt x is to be real.

    then sqrt x is from 0 to + oo
    e^0 = 1
    so range would be from 1 to infinity

    2. f' = e^sqrt x * d/dx (x^1/2)
    =e^sqrt x * (1/2) x^-1/2
    = 2 e^sqrt x / sqrt x

    3. f' looks always positive to me

    ----------------------------
    e^x + 1/e^x

    think x = - some big number
    say -100
    then it is e^-100 + e^100
    think x the same + big number
    then it is e^100 + e^-100
    the same y for + 100 and -100 and positive for both

    now what if x is + or - 1
    then it is e + 1/e around 3

    now what if x = 0
    1 + 1/1 = 2

    so
    domain is all real x
    range is all y ≥ 2

    I think you can do the rest now

  • Calculus - please help -

    a) y = e^(√x)

    1. clearly x≥0 for the square root of x to be defined, so the domain is x ≥ 0
    range : y ≥ 1
    2. y' = (1/2)x^(-1/2)(e^(√x))
    = 1/(2√x)(e^√x)
    3. the graph is contantly increasing, never decreases


    b) this is the equation of a "catenary", or the shape formed when a chain is allowed to hang freely.

    it has a vertex when x = 0 giving f(0)= 2. Domain : x any real number, range : y ≥ 2

    f'(x) = e^x - e^-x

    for x < 0 the function is decreasing (the first derivative is negative)
    and for x > 0 the function is increasing, because the derivative is positive.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Calculus

    Let f(x) = -2/((5+3x)^4) Determine f'(x) using the chain role. Can someone please do this step by step and explain?
  2. Calculus

    Find the equation of the tangent to the curve y=2-e^-x at the point where x=1. Can someone please do this step by step and explain?
  3. Algebra help

    f(x)=x^3-4x^2-x+4 How do I find the x-intercept for this?
  4. Algebra

    Totally confused and have 5 more problems like this. Can someone explain each step for these questions?
  5. Physics

    Can someone please show me step by step how to normalize e^-5x in the interval (0, infinity)?
  6. Calculus

    Find the volume of the solid obtained by rotating the region bounded by y=x^3, y=1, and the y-axis around the x-axis. What I did was: V=ç(0,1)pi(1-x^3)^2 dx v=pi(x^7/7-x^4/2+x) and I evaluated it for one since 0 is just going to …
  7. algebra-trig

    Can someone please explain to me how to graph sine and cosine step by step because I am so confused and I really really need help.
  8. algebra-trig

    Can someone please explain to me how to graph sine and cosine step by step because I am so confused and I really really need help.
  9. Calculus

    Find DOMAIN and RANGE of the following: a) f(x)= 3/(|x+3|) b) 1/(cube root of 9x-x^2) c) ln(9x+x^2) Please help, I have no idea how to find domain and range of these. Step-by-step would be really helpful. Thank you so much!
  10. Math

    I need help solving the problem not the answer. (Multiple Choice) The steps below show the incomplete solution to find the value of x for the equation 7x + 8 − 3x = −6 + 10: Step 1: 7x + 8 − 3x = −6 + 10 Step 2: 7x + 8 − …

More Similar Questions