다항함수 미분계수 계산

문제

함수 $f(x) = x^3 - 2x^2 + 5$에 대하여 $f'(1)$의 값은?

<!-- X-축 눈금 및 라벨 -->
<line x1="100" y1="245" x2="100" y2="255"/>
<text x="100" y="270" fill="#1F2937" font-size="12px" text-anchor="middle">1</text>
<line x1="150" y1="245" x2="150" y2="255"/>
<text x="150" y="270" fill="#1F2937" font-size="12px" text-anchor="middle">2</text>

<!-- Y-축 눈금 및 라벨 -->
<line x1="45" y1="220" x2="55" y2="220"/>
<text x="30" y="225" fill="#1F2937" font-size="12px" text-anchor="end">1</text>
<line x1="45" y1="190" x2="55" y2="190"/>
<text x="30" y="195" fill="#1F2937" font-size="12px" text-anchor="end">2</text>
<line x1="45" y1="160" x2="55" y2="160"/>
<text x="30" y="165" fill="#1F2937" font-size="12px" text-anchor="end">3</text>
<line x1="45" y1="130" x2="55" y2="130"/>
<text x="30" y="135" fill="#1F2937" font-size="12px" text-anchor="end">4</text>
<line x1="45" y1="100" x2="55" y2="100"/>
<text x="30" y="105" fill="#1F2937" font-size="12px" text-anchor="end">5</text>

<!-- 원점 O 라벨 -->
<text x="40" y="265" fill="#1F2937" font-size="14px">O</text>

<!-- 축 라벨 -->
<text x="360" y="255" fill="#1F2937" font-size="14px">x</text>
<text x="55" y="15" fill="#1F2937" font-size="14px">y</text>

<!-- 함수 f(x) = x^3 - 2x^2 + 5 그래프 경로 -->
<!-- x 범위: -0.5 ~ 2.5, y 스케일: x축 1단위 = 50px, y축 1단위 = 30px, 원점 (50, 250) -->
<path d="M 25.000 118.750 L 27.500 111.520 L 30.000 105.000 L 32.500 99.188 L 35.000 94.063 L 37.500 89.600 L 40.000 85.763 L 42.500 82.525 L 45.000 79.850 L 47.500 77.713 L 50.000 100.000 L 52.500 104.125 L 55.000 104.188 L 57.500 104.538 L 60.000 105.188 L 62.500 106.150 L 65.000 107.438 L 67.500 109.063 L 70.000 111.038 L 72.500 113.375 L 75.000 116.088 L 77.500 119.188 L 80.000 122.688 L 82.500 126.595 L 85.000 130.925 L 87.500 135.688 L 90.000 140.888 L 92.500 146.538 L 95.000 152.650 L 97.500 159.238 L 100.000 130.000 L 102.500 128.875 L 105.000 127.788 L 107.500 126.725 L 110.000 125.663 L 112.500 124.588 L 115.000 123.475 L 117.500 122.300 L 120.000 121.038 L 122.500 119.663 L 125.000 118.150 L 127.500 116.475 L 130.000 114.613 L 132.500 112.538 L 135.000 110.213 L 137.500 107.600 L 140.000 104.663 L 142.500 101.375 L 145.000 97.700 L 147.500 93.600 L 150.000 100.000 L 152.500 94.125 L 155.000 88.000 L 157.500 81.625 L 160.000 75.000 L 162.500 68.125 L 165.000 61.000 L 167.500 53.625 L 170.000 46.000 L 172.500 38.125 L 175.000 6.250"/>

<!-- 접선 (y = -x + 5) - 점선으로 표시 -->
<line x1="25" y1="85" x2="175" y2="175" stroke-dasharray="5 5"/>

<!-- 접선의 기울기 라벨 -->
<text x="130" y="145" fill="#6C63FF" font-size="12px">m = -1</text>