第 1 題
1 分Find the derivative of the function \( f(x) = 4x^3 - 2x^2 + 7x - 5 \) with respect to \( x \).
Cambridge International AS Level · Mathematics (9709)
Differentiation：練習題
5 條多項選擇題即時批改，另有 4 條文字題附完整解題步驟，全部圍繞「Differentiation」。
9 條題目21 分免費，無需登記
第 2 題
1 分Find the x-coordinate of the local minimum point of the curve \( y = x^3 - 3x^2 - 9x + 5 \).
第 3 題
1 分The radius \( r \) of a circle is increasing at a constant rate of \( 0.5 \text{ cm s}^{-1} \). Find the rate of increase of the area \( A \) of the circle at the instant when the radius is \( 10 \text{ cm} \).
第 4 題
1 分Find the gradient of the curve \( y = 3x^2 - 5x + 2 \) at the point \( (2, 4) \).
第 5 題
1 分Using the chain rule, find the derivative \( \frac{dy}{dx} \) for the function \( y = \sqrt{4x^2 + 9} \).
第 6 題
2 分Find the gradient of the curve \(y = 3x^2 - 5x + 2\) at the point where \(x = 2\).
先自己寫一次答案，再對照解題步驟。
第 7 題
3 分Find the derivative \(\frac{dy}{dx}\) of the function \(y = \sqrt{2x^3 + 5}\) using the chain rule.
先自己寫一次答案，再對照解題步驟。
第 8 題
6 分Find the coordinates of the stationary point on the curve \(y = x^2 + \frac{16}{x}\) for \(x > 0\) and determine its nature using the second derivative.
先自己寫一次答案，再對照解題步驟。
第 9 題
5 分A curve has the equation \( y = 2x^3 - 9x^2 + 12x - 5 \).
(a) Find an expression for \( \frac{dy}{dx} \).
(b) Find the \( x \)-coordinates of the stationary points on the curve.
(c) Use the second derivative \( \frac{d^2y}{dx^2} \) to determine the nature of each stationary point.
先自己寫一次答案，再對照解題步驟。
* thinka提供的內容由AI生成，可能並非總是準確或最新。請將其用作輔助資源，並與官方材料進行核實。
想多做幾條同類題目？立即開始練習呢個課題，即做即批改。
立即練習