If f (x) = 3x2+15x+5, then the approximate value of f (3.02) is
If f (x) = 3x2+15x+5, then the approximate value of f (3.02) is
- 47.66
- 57.66
- 67.66
- 77.66
The Correct Option is D
Solution and Explanation
Let x = 3 and ∆x = 0.02. Then, we have
f(3.02)=f(x+Δx)=3(x+Δx)2+15(x+Δx)+5
Now,Δy=f(x+Δx)-f(x)
=f(x-Δx)=f(x)+Δy
≈f(x)+f'(x)Δx (As dx=Δx)
f(3.02)=(3x2+15x+5)+(6x+15Δx)
77.66
Hence, the approximate value of f(3.02) is 77.66.
The correct answer is D.
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Notes on Applications of Derivatives
Concepts Used:
Application of Derivatives
Various Applications of Derivatives-
Rate of Change of Quantities:
If some other quantity ‘y’ causes some change in a quantity of surely ‘x’, in view of the fact that an equation of the form y = f(x) gets consistently pleased, i.e, ‘y’ is a function of ‘x’ then the rate of change of ‘y’ related to ‘x’ is to be given by
\(\frac{\triangle y}{\triangle x}=\frac{y_2-y_1}{x_2-x_1}\)
This is also known to be as the Average Rate of Change.
Increasing and Decreasing Function:
Consider y = f(x) be a differentiable function (whose derivative exists at all points in the domain) in an interval x = (a,b).
- If for any two points x1 and x2 in the interval x such a manner that x1 < x2, there holds an inequality f(x1) ≤ f(x2); then the function f(x) is known as increasing in this interval.
- Likewise, if for any two points x1 and x2 in the interval x such a manner that x1 < x2, there holds an inequality f(x1) ≥ f(x2); then the function f(x) is known as decreasing in this interval.
- The functions are commonly known as strictly increasing or decreasing functions, given the inequalities are strict: f(x1) < f(x2) for strictly increasing and f(x1) > f(x2) for strictly decreasing.
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