Calculusantiderivative
posted by Callie
Find f.
f ''(θ) = sin θ + cos θ, f(0) = 5, f '(0) = 3
My steps:
f'(θ)=cosθsinθ+C
When f'(0)=3, C=2, so f'(θ)=cosθsinθ2.
f(θ)=sinθcosθ2x+D
When f(0)=5, D=6, so f is sinθcosθ2x+6.
How is that wrong?

Reiny
f'Ø) = cosx + sinx + C
you differentiated instead of integrated.
Had you checked your answer by taking the derivative you would have seen your error
since f'(0) = 3
3 = cos0 + sin0 + c
3 = 1 + 0 + c > c = 4
so f'(x) = cosx + sinx + 4
f(x) = sinx  cosx + 4x + d
and f(0) = 5
5 = sin0  cos0 + 0 + d
5 = 0  1 + d
d = 6
f(x) = sinx  cosx + 4x + 6
Just realized I used x instead of Ø, no big deal to change
I suggest you take a better look at the derivatives of both sine and cosine
Respond to this Question
Similar Questions

Math  Calculus
The identity below is significant because it relates 3 different kinds of products: a cross product and a dot product of 2 vectors on the left side, and the product of 2 real numbers on the right side. Prove the identity below.  a … 
math
if cosθ=2/3 and tanθ<0 find the exact value sin(θ5π/3) sin2θ cos2θ cos(θ/2) can some1 please help me? 
trigonometry
if cosθ=2/3 and tanθ<0 find the exact value sin(θ5π/3) sin2θ cos2θ cos(θ/2) can some1 please help me? 
Trigonometry
Which of the following is equivalent to 1 − cos 2 θ/cos 2 θ? 
Calculus AP
hi again im really need help TextBook: James Stewart:Essential Calculus, page 311. Here the problem #27: First make a substitution and then use integration by parts to evaluate the integral. Integral from sqrt(pi/2) TO sqrt(pi)of θ^3 … 
Trigonometry
There are four complex fourth roots to the number 4−4√3i. These can be expressed in polar form as z1=r1(cosθ1+isinθ1) z2=r2(cosθ2+isinθ2) z3=r3(cosθ3+isinθ3) z4=r4(cosθ4+isinθ4), … 
Trig
Given that csc θ = 4 and tan θ > 0, find the exact value of a. x b. sin θ c. cos θ d. r e. sec θ f. cot θ 
2 math ?s
Thank you so much in advance! Verify each identity. Work one side (the harder side) Please show me the work sin θ +cos θ cot θ= csc θ Cos^2 θ + 1 =2cos^2 θ +sin^2 θ 
Math Question
Given tan θ = 8/5 and sin θ < 0, find sin θ, cos θ, csc θ, sec θ, and cot θ. 
PRECALC
solve the equation 1. cos(θ) − sin(θ) = 1 2.2 cos(θ) tan(θ) + tan(θ) = 1 + 2 cos(θ) 3. sin(θ) cos(3θ) + cos(θ) sin(3θ) = 0 4. sin(2θ) cos(θ) − cos(2θ) sin(θ) …