Question

Найти углрвой коэффициент спасательной к графику функции -3х^2+2х-1 в точке х=-5

Answer 1

F(x)-3x²+2x-1    x=-5
f`(x)=6x+2
f(-5)=6*(-5)+2=-30+2=-28
Ответ:  угловой коэффициент касательной равен -28.

Answer 2

Finding the Derivative and Evaluating at a Specific Point

To find the derivative of the function f(x) = -3x^2 + 2x - 1, we can use the power rule for differentiation. The power rule states that for a function of the form f(x) = ax^n, the derivative is given by f'(x) = nax^(n-1).

Applying the power rule to our function, we have:

f'(x) = d/dx (-3x^2) + d/dx (2x) + d/dx (-1)

Simplifying each term, we get:

f'(x) = -6x + 2

Now, we can evaluate the derivative at the specific point x = -5. Substituting x = -5 into the derivative, we have:

f'(-5) = -6(-5) + 2

Simplifying further, we get:

f'(-5) = 30 + 2

f'(-5) = 32

Therefore, the derivative of the function -3x^2 + 2x - 1 is -6x + 2, and when evaluated at x = -5, the derivative is 32.