Please, help me with this problem:
frind the derivative of each function at the given number.
21. f(x)= -4x + 5 at 3
22. f(x)= -4 + 3x at 1
thanks
Both of your equations are straight lines.
So they have the same slope no matter where you are on the line
21. y = -4x + 5
compare with y = mx + b, where m is the slope
slope = -4
let me know what you got for 22.
Sure! I can help you find the derivative of each function at the given number.
To find the derivative of a function, we can apply the power rule. The power rule states that if we have a function of the form f(x) = ax^n, where a is a constant and n is any real number, then the derivative of f(x) is given by f'(x) = anx^(n-1).
Let's solve each problem step-by-step:
21. f(x) = -4x + 5 at x = 3
To find the derivative, we'll differentiate each term separately. Since -4x is multiplied by 1, its derivative will be -4 * 1 = -4. And since 5 is a constant, its derivative will be 0.
Therefore, the derivative of f(x) = -4x + 5 is f'(x) = -4.
22. f(x) = -4 + 3x at x = 1
Using the power rule, the derivative of -4 is 0, since it is a constant. The derivative of 3x is 3, since the coefficient of x is 3 and the derivative of x is 1.
Therefore, the derivative of f(x) = -4 + 3x is f'(x) = 3.
So, the derivatives of the given functions at the specified numbers are:
21. f'(3) = -4
22. f'(1) = 3
To find the derivative of a function at a given number, you can use the concept of the derivative, which measures the rate of change of a function at any point.
For the first problem, we need to find the derivative of the function f(x) = -4x + 5 at x = 3. The derivative of a linear function (in this case, -4x + 5) is simply the coefficient of the x term, which is -4. Therefore, the derivative of f(x) = -4x + 5 is -4. Hence, at x = 3, the derivative of f(x) is -4.
For the second problem, we need to find the derivative of the function f(x) = -4 + 3x at x = 1. Again, the derivative of a linear function is the coefficient of the x term, which is 3 in this case. Therefore, the derivative of f(x) = -4 + 3x is 3. Hence, at x = 1, the derivative of f(x) is 3.