Nawz said:Homework Statement
Use a calculator to estimate any extrema of this function:
f(x)=5x^3-30x^2+45x+5(sqrt(x))
Homework Equations
The Attempt at a Solution
I don't know how to find it using a calculator.
f'(x)= 15x^2-60x+45+(5/2)x^(-1/2)
The purpose of using a calculator to estimate extrema in calculus is to quickly and accurately identify the maximum and minimum values of a function. This can be useful in many real-world applications, such as optimizing a business's profits or determining the ideal conditions for a scientific experiment.
A calculator uses numerical methods, such as the Newton-Raphson method, to find the roots of a function. The roots of a function correspond to the x-values where the function's slope is equal to zero, which is where the function reaches its maximum or minimum value.
No, a calculator may not always be accurate when estimating extrema in calculus. This is because numerical methods can sometimes give approximate solutions, rather than exact ones. Additionally, the accuracy of the estimation may depend on the precision of the calculator and the complexity of the function being evaluated.
Yes, a calculator can estimate extrema for any type of function, including polynomial, exponential, trigonometric, and logarithmic functions. However, the method used to estimate the extrema may vary depending on the type of function.
One limitation of using a calculator to estimate extrema in calculus is that it cannot always find the global maximum or minimum of a function. In some cases, the function may have multiple local extrema, and a calculator may only be able to find one of them. Additionally, a calculator may not be able to find extrema for functions with discontinuities or undefined points.