Вопрос школьника по предмету Математика
для графика функции y=8x — x^4
a) запишите уравнение касательной в точке с абсциссой х0=1
б) найдите тангенс угла наклона касательной к оси Ох в точке с абсциссой х0=0
Ответ учителя по предмету Математика
а) координаты точки касания
f(x0)=8*x₀-(x₀)⁴=8*1-1⁴=8-1⁴=7
точка касания (1;7)
найдем коэфициент к касательной он равен значению производной в этой точке
f'(x)=(8x-x⁴)’=8-4x³
f'(x₀)=8-4(x₀)³=8-4*1³=8-4=4
k=4
зная координаты точки касания найдем значение в
x₀=1 y₀=7
у=кх+в
7=4*1+в
в=7-4=3
уравнение касательной
у=4х+3
б)
тангес угла наклона касательной есть значение производной в данной точке
f'(x₀)=8-4*x₀³=8-4*0³=8
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