Question

Найди угловой коэффициент касательной к графику функции f(x)=3x во второй степени + 7х+9 в точке с абсциссой х0=0 нужен подробный ответ(полное решение)

Answer 1

Ответ:

7

Пошаговое объяснение:

k=f `(x₀)

f(x)=3x²+7x+9

f `(x)=(3x²+7x+9)`=3*2x+7=6x+7

x₀=0

f `(x₀)=f `(0) = 6*0+7=0+7=7

k=7

Answer 2

Finding the Slope of the Tangent Line

To find the slope of the tangent line to the graph of the function f(x) = 3x^2 + 7x + 9 at the point with x-coordinate x0 = 0, we can use the derivative of the function. The derivative gives us the rate of change of the function at any given point.

The derivative of the function f(x) = 3x^2 + 7x + 9 can be found by applying 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 a real number, then the derivative is given by f'(x) = nax^(n-1).

Applying the power rule to the function f(x) = 3x^2 + 7x + 9, we get:

f'(x) = 2 * 3x^(2-1) + 1 * 7x^(1-1) + 0 = 6x + 7

Now, to find the slope of the tangent line at x = x0 = 0, we substitute x = 0 into the derivative:

f'(0) = 6(0) + 7 = 7

Therefore, the slope of the tangent line to the graph of the function f(x) = 3x^2 + 7x + 9 at the point with x-coordinate x0 = 0 is 7.

Answer: The slope of the tangent line to the graph of the function f(x) = 3x^2 + 7x + 9 at the point with x-coordinate x0 = 0 is 7.

Explanation of the Solution

To find the slope of the tangent line, we used the derivative of the function. The derivative gives us the rate of change of the function at any given point. By applying the power rule to the function f(x) = 3x^2 + 7x + 9, we found the derivative f'(x) = 6x + 7. Substituting x = 0 into the derivative, we obtained f'(0) = 7, which is the slope of the tangent line at x = 0.

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