Find f such that the given conditions are satisfied.
$$ f(x)=x^{2}-3 x+9, f(0)=5 $$
\(f(x)=\frac{1}{3} x^{3}-\frac{3}{2} x^{2}+9 x+5\)
\(f(x)=\frac{1}{3} x^{3}-4 x^{2}+9 x+5\)
\(f(x)=\frac{1}{3} x^{3}-\frac{3}{2} x^{2}+9 x+1\)
\(f(x)=\frac{1}{3} x^{3}-4 x^{2}+9 x+1\)
Let, f'(x) = x2 - 3x + 9
integrate both sides with respect to 'x',
∫f'(x) = ∫(x2 - 3x + 9)dx
=>f(x) = ∫(x2)dx - 3∫(x)dx + 9∫dx
=>f(x) = x3/3 - (3/2)x2 + 9x + C
if f(0) = 5, then,
(0)3/3 - (3/2)(0)2 + 9(0) + C = 5
=> C = 5
therefore, f(x) = x3/3 - (3/2)x2 + 9x + C
the first option is your answer.
Find f such that the given conditions are satisfied. f'(x)=x-5, f(3) = 3 O A. 1x) = + 5x+ OB. f(x)=x2 -5% O c. f(x)=x2 –5x+9 OD. 1x) = -5x +
Find f such that the given conditions are satisfied. f'(x)=x-8, f(5)= - 14 O A. f(x) = x? - 8x OB. f(x)= x? –8x +1 Oc. (x) = 1 / - 6x + 2 / 2 o
1-Given the function: \(y=\frac{x^{2}-3 x-4}{x^{2}-5 x+4}\), decide if \(f(x)=y\) is continuous or has a removable discontinuity, and find horizontal tond vertical asymptotes.2 A-Use the definition \(\lim _{h \rightarrow 0} \frac{f(x+h)-f(x)}{h}\) to prove that derivative of \(f(x)=\sqrt{4-x}\) is \(\frac{-1}{2 \sqrt{4-x}}\)2 B- Evaluate the limit \(\lim _{h \rightarrow 0} \frac{f(x+h) - f(x)}{h}\) for the given value of \(x\) and function \(f(x) .\)$$ f(x)=\sin x, \quad x=\frac{\pi}{4} $$3-Given the function: \(y=(x+4)^{3}(x-2)^{2}\), find y' and classify critical numbers very carefully using first derivative tess...
Find the complete factored form of the polynomial f(x) that satisfies the given conditions. Degree 3, leading coefficient -5, zeros at 9,2-8 i and 2 +8 i. O A. f(x)= - 5(x- 9)(x2 - 4x +68) OB. f(x) = -5(x +9)(x - 2 - 8i)(x - 2 +81) O c. f(x) = -5(x -9)(x - 2 - 8 i)(x - 2 + 8 i) OD. f(x) = - 5(x +9)(x2 - 4x+68)
Given the set of information, find a linear equation f(x) satisfying the conditions, if possible. (If not possible, enter IMPOSSIBLE.) f(−4) = 6 and f(5) = 3
6. Find the exact value of ,* f'(x) dx, if the graph of f(x) is given below. 6 5 3 3 2 1 0 2 3 4 5 6 7 8 9
Find an equation of the line that satisfies the given conditions. Through (-1, -14); perpendicular to the line passing through (2,-2) and (6,-4) Find an equation of the line that satisfies the given conditions. Through (-9, 1); parallel to the line x = 7 Find an equation of the line that satisfies the given conditions. Through (1, 1); parallel to the line y = 9x - 7 Find an equation of the line that satisfies the given conditions. Through (9,...
Find a polynomial function of degree 3 with real coefficients that satisfies the given conditions. See Example 4. 5) Zeros of 2 f (x) = - 3 and 5: f(3) = 6
5. Find the particular solution of the equation, S'(x) = 63% conditions f(1) = 2. that satisfies the 6. Find y = f(x), if f "(x) = 4x +3, f(1)=5, f(0)= -6 7. Evaluate: (4x + 3x)dx. Give a numeric answer/ Simplify. 8. Given: f(x)= e' + F(5)= 148.21, find F(1) 9. A concert hall is filling with people from noon until show time at 3:00 pm. The table below shows the rate of people entering the concert hall (measured...
Let \(f(x)= \begin{cases}0 & \text { for } 0 \leq x<2 \\ -(4-x) & \text { for } 2 \leq x \leq 4\end{cases}\)- Compute the Fourier cosine coefficients for \(f(x)\).- \(a_{0}=\)- \(a_{n}=\)- What are the values for the Fourier cosine series \(\frac{a_{0}}{2}+\sum_{n=1}^{\infty} a_{n} \cos \left(\frac{n \pi}{4} x\right)\) at the given points.- \(x=2:\)- \(x=-3\) :- \(x=5:\)